Author: James Glover
Publication: The Hindu
Date: October 15, 2014
URL: http://www.thehindu.com/opinion/oped/everythingvedicinvedicmaths/article6500986.ece?homepage=true
It uses short and efficient aphorisms to express principles and rules
In the light of the Human Resources Development Minister Smriti Irani bringing to the forefront the need for some Indianisation of the school curriculum, together with the inclusion of Vedic Maths, it is necessary for a greater understanding of what this subject is about. To date, there has been a groundswell of grassroots interest in this, particularly in India, but there has also been serious criticism of its “Vedicness.”
This criticism was recently highlighted in an article in The Hindu by Professor C.K. Raju (“Nothing Vedic in ‘Vedic Maths,’” Sept. 3) which, unfortunately, was a misunderstanding of what this approach to Maths is really about and what constitutes the Vedas.
A holistic approach
Vedic Maths is concerned with a universal structure of Maths revealed through a personal approach to problemsolving and other fields of human activity. It is described by a small collection of aphorisms called sutras. Sutras express naturally occurring mental processes by which mathematical problems can be solved with the least effort. Vedic Maths does not advocate the sole use of blanket methods through which students can reduce problems to merely mechanical responses to given stimuli. Instead, it encourages an intelligent and holistic approach — one that engenders reason and develops strategic thinking. There are blanket methods as well as special case methods. If you find that a problem can be solved by an easier or different method from what is commonly taught, then that is used as a valid method, even if the problem is solved just by inspection. The sutras describe such principles and methods.
For example, if you want to add 324 and 199, an easy approach is to add 200 instead of 199 to 324 and take off one, resulting in 523. This is a naturally occurring mental method and uses the fact that 199 is deficient from 200 by one. Such special cases are not normally taught but most people will naturally adopt them by understanding numbers. This comes under the pithy sutra, deficiency. This example shows that there are often simple methods which follow the path of least action and reflects Sir Isaac Newton’s observation, “Nature abhors the pomp of superfluous causes.”
Each sutra covers a wide range of applications, and the recognition of the same underlying thought pattern at work has the effect of unifying diverse aspects of Maths. An example of this is the Paravaryta Yojayet sutra, meaning ‘transpose and adjust’. It occurs wherever there is an action by which something is transferred to something else with a resulting adjustment. Such is the case when an architect transposes a previously used plan to a new situation or a doctor adjusts a common prescription to suit the needs of an individual. The mathematical applications of this sutra are manifold such as for transformations, equations, polynomial division, matrices, analytic geometry, calculus, and many others.
It must be emphasised that Vedic Maths highlights the mental processes and principles that take place in the mind of anyone engaged in mathematical activity. These processes are not random and haphazard but are reasonable, ordered and yet highly flexible.
The sutras also reflect deeper philosophical truths concerning human nature, our perception of the world and our relationship with it. For example, one sutra states Vyashti Samashti, Specific and General. A simple application is in finding a mean, which provides a single number that represents the whole. It describes the principle in which something of the whole is reflected in the part or individual — a wideranging law or principle permeating throughout nature. For example, oak trees have characteristics common to all trees of that genre and yet each oak tree is different from every other. The commonality is reflected in each individual. The same principle occurs in the Egyptian, Hermetic, Platonic, Hindu, Judaic, Islamic and Christian teachings often expressed as “As above, so below.”
To the outsider or casual onlooker Vedic Maths appears to be a collection of arithmetic maths tricks and algebraic methods but this is very far from the truth about the system. Critics of Vedic Maths have not examined what it is really about —like judging soup by reading the ingredients of the label on the tin rather than tasting what is inside.
Prof. Raju claims that Bharati Krishna Tirtha’s book “Vedic Mathematics” states that the sutras are not to be found in the Vedas. In fact the general editor of the text states that this work “deserves to be regarded as a new Parishishta [appendix to the Vedas] by itself” since it is not to be found in any known or published Parishishtas. However, on page 231 of “Vedic Metaphysics,” Tirthaji states that he found all 16 sutras in the SthapatyaVeda in connection with astronomy. It is quite feasible that this is not a published source. Nevertheless, the indication is that Prof. Raju thinks the Vedas are a fixed set of texts from antiquity and that they are published and can be searched through. But this is not so. Yes, there are ancient texts commonly accepted as Vedic but there are other treatises, or expressions, which may constitute Vedas — those that are not published or even translated from the original Sanskrit language.
More importantly, such critics rely on only one narrow interpretation of what constitutes the Vedas. Clearly, in India, there is great emotive connection with the understanding that Vedas are ancient texts forming the basis for culture, laws, morals, religion and philosophy. But to understand really what the Vedas are, we should seek out authority on the matter rather than rely on mathematicians, journalists, historians, and so forth. In 1965, the same year that Tirthaji’s book was published, Shankaracharya Shantananda Saraswati, famous for his profound understanding of Vedic philosophy, the spread of meditation and his connections with seekers of spiritual knowledge from the West, said, “The Veda should not be taken in a very restricted sense. The Veda means knowledge and it is not entirely Indian. It manifests in many ways in different lands. Any nation or race or group of people who have learned to live a civilised life; who have evolved or appreciated ethics or morals, govern themselves according to laws, they too have seen the Vedas. It may be different, but nevertheless it is the Veda. The West is neither entirely destitute of Vedas...They, and many others too, have some part of the universal knowledge.” Here Vedas mean universal knowledge and are not restricted to a hoary past. Vedas are living knowledge and not something from history. Part of the civilised life, to which the Shankaracharya refers, is the use and development of reason. This includes Maths. And people’s personal experience of revelation or realisation in Maths seems to be connected with that “wow” moment when something is suddenly seen to be true.
Offering a new orientation
Prof. Raju’s expertise and knowledge of the history of Indian mathematics is of the highest standard. He points out that India has a brilliant past with regard to the development of Maths. So much so that even now there are research programmes, for example at IIT in Mumbai, looking into the vast knowledgebase of the mathematics of Kerala spanning nearly a 1,000 years. But the history of Maths is not what Vedic Maths is about at all. These sutras of Tirthaji reveal the real deal; they show the principles and laws behind mathematics and mathematical activity as it happens in the present. Vedic Maths is not historical and is not about mathematical tricks. It provides deep insights into the very nature of the subject and the human psyche. Neither is it exclusive. Although Tirthaji sets out alternative methods for some topics, he does not exclude more widely known methods. Rather it expresses underlying laws and mental patterns of all methods. It provides us with an entirely new orientation — one that humanises mathematics, thereby reducing fear of numbers and mathematical concepts.
Vedic Maths unifies diversity, uses short and efficient aphorisms to express principles and rules of working, produces and encourages easy routes for problemsolving, develops strategic thinking, describes what happens in the mind as mathematics happens, and points to underlying spiritual truths.
Ms Irani has every right to explore the avenues which this new and attractive approach to Maths offers. It will be interesting to see how this unfolds in schools. Having taught Vedic Maths for more than 30 years in the U.K. and other countries, I have seen students of all ages finding nothing but delight in this system. Moreover, they have benefited from it.
(James Glover is a fellow of the Institute of Mathematics and its Applications. He is the author of Vedic Mathematics for Schools, 13.)
